Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B'A) Given the matrices 1 0 2 -1 2 1 1 -2 1 2 -3 A B and C = 0 3 1 0 -1 determine (A, Β (A+B, C ) || A ||2 , || B |2 and cos(0), where O is the angle between matrices A and B ||

Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B'A) Given the matrices 1 0 2 -1 2 1 1 -2 1 2 -3 A B and C = 0 3 1 0 -1 determine (A, Β (A+B, C ) || A ||2 , || B |2 and cos(0), where O is the angle between matrices A and B ||

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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Question

Linear Algebra

Consider the real vector space M2x3(R) with the usual inner product
(A, B) = tr (B'A)
Given the matrices
1 0 2
-1 2 1
1 -2 1
2 -3
A
B
and C =
0 3
1
0 -1
determine
(A, Β
(A+B, C )
|| A ||2 , || B |2
and cos(0),
where O is the angle between matrices A and B
||

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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